Police are considering a petition calling for a probe against Future Forward Party leader Thanathorn Juangroongruangkit and two others for allegedly offending late statesman Prem Tinsulanonda via social media.
New Alternative Party founder Rachen Trakulwiang was referring to posts that he claimed were attacks on Gen Prem, as he made the complaint at the Technology Crime Suppression Division on Tuesday.
"Gen Prem was a representative of the King. We should treat him with respect," said Mr Rachen as his group Khon Rak Pa ("People Who Love Pa", the nickname of Gen Prem).
Other suspects who face similar allegations are Parit "Penguin" Chiwarak, an anti-coup activist who chairs the Student Union of Thailand, and Suphraiphon Chuaichu, a losing Puea Chat Party election candidate for Bangkok's Bang Khunthian district.
Gen Prem served as president of the Privy Council before he passed away on May 26, and Mr Rachen said he suspected their alleged insults could be the start of attempts to destroy the Privy Council and the military.
"We can't accept that and will never let it happen," he said, adding that his group had urged police to take legal action.